Two circles are externally tangent at point P, as shown. Segment CPD is parallel to common external tangent . Let be M on AB so that MP is tangent to both circles.
(a) Prove that M is the midpoint of AB.
(b) Let Q be the intersection of AC and BD. Show that triangle QAB is congruent to triangle PAB.
(c) Let N be the midpoint of CD. Show that MN = AB/2.